Exercise 10.1

centre (0,2) and radius 2 2. centre (-2,3) and radius 4

Represent graphically a displacement of 40 km, 30° east of north.

How many tangents can a circle have?

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x + y = 16.

Find the equation of the circle passing through the points (2,3) and (-1,1) and whose centre is on the line x - 3y - 11 = 0.

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3).

Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

Find the equation of a circle with centre (2,2) and passes through the point (4,5).

Does the point (-2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25? Fig 10. 13

Fill in the blanks :

(i) A tangent to a circle intersects it in ______ point(s).

(ii) A line intersecting a circle in two points is called a ______.

(iii) A circle can have ______ parallel tangents at the most.

(iv) The common point of a tangent to a circle and the circle is called ______.

Classify the following measures as scalars and vectors. (i) 10 kg (ii) 2 meters north-west (iii) 40° (iv) 40 watt (v) 10-19 coulomb (vi) 20 m/s2

centre ( 1,2 1 ) and radius 1 4. centre (1,1) and radius 2

A tangent $PQ$ at a point $P$ of a circle of radius $5$ cm meets a line through the centre $O$ at a point $Q$ so that $OQ = 12$ cm. Length $PQ$ is :

(A) $12$ cm    (B) $13$ cm    (C) $8.5$ cm    (D) $119$ cm.

Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force (iv) velocity (v) work done

In Fig 10.6 (a square), identify the following vectors. (i) Coinitial (ii) Equal (iii) Collinear but not equal

Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

centre (-a, -b) and radius 2 2b a− . In each of the following Exercises 6 to 9, find the centre and radius of the circles.

Answer the following as true or false. (i) and - are collinear. (ii) Two collinear vectors are always equal in magnitude. (iii) Two vectors having same magnitude are collinear. (iv) Two collinear vectors having the same magnitude are equal.

(x + 5)2 + (y - 3)2 = 36 7. x2 + y2 - 4x - 8y - 45 = 0

x2 + y2 - 8x + 10y - 12 = 0 9. 2x2 + 2y2 - x = 0